Patch-density in tensor-triangular geometry

2025/03/19 by Balmer, Paul, Gallauer, Martin · 2 citations
#Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2503.15274

Abstract

The spectrum of a tensor-triangulated category carries a compact Hausdorff topology, called the constructible topology, also known as the patch topology. We prove that patch-dense subsets detect tt-ideals and we prove that any infinite family of tt-functors that detects nilpotence provides such a patch-dense subset. We review several applications and examples in algebra, in topology and in the representation theory of profinite groups.

Cited by

• Re-framing the classification of ideals in noncommutative tensor-triangular geometry
• On functoriality and the tensor product property in noncommutative tensor-triangular geometry

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